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Updated: Sep 2, 2025

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
Published on: October 12, 2019
The generalized method to calculate the real-space winding number for one-dimensional systems with complex
Yu Zhang1,2,3, Langlang Xiong1,3, Xunya Jiang1,2,3
1Engineering Research Center of Advanced Lighting Technology, Ministry of Education, Fudan University, Shanghai 200433, People's Republic of China.
A new method accurately calculates topological invariants in complex 1D systems with multiple band gaps, like quasi-crystals. This approach predicts topological phase transitions and fractional charges, advancing the study of complex materials.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Topological Matter
Background:
- Topological studies of complex 1D systems with multi-band-gap structures are challenging due to the lack of effective topological invariants.
- Quasi-crystals (QCs) and intricate periodic models present difficulties in characterizing topological properties.
Purpose of the Study:
- To propose a generalized method for calculating the real-space winding number in complex 1D systems with multi-band-gap structures.
- To demonstrate the method's effectiveness in predicting topological phase transitions and fractional edge charges.
- To apply the method to Thue-Morse (TM) quasi-crystalline systems.
Main Methods:
- A generalized method based on the contracted wave-function is developed.
- The real-space winding number is calculated for various gaps in 1D systems.
- The method is applied to the 4-atom SSH model and 1D Thue-Morse systems.
Main Results:
- The generalized method successfully obtains quantized real-space winding numbers for traditional and fractal gaps.
- It accurately predicts topological phase transitions and fractional charges (including 1/4) in the 4A-SSH model.
- New phenomena like topological phase transitions in multi-band-gap structures and asymmetric fractional charges in TM systems are observed.
Conclusions:
- The generalized method is a powerful tool for studying the topology of gaps in complex periodic systems and quasi-crystals.
- It provides a robust framework for understanding topological properties in intricate 1D materials.
- The findings open new avenues for exploring topological phenomena in advanced materials.
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